1. Field of the Invention
The present invention relates to a position control apparatus for a ball screw drive system.
2. Description of the Prior Art
FIG. 1 of the accompanying drawings shows a general mechanism of a ball screw drive system about one axis. When a servomotor 100 rotates, gear train 101a, 101b having a gear ratio of 1:n and serving as a reduction gear connected to the servomotor 100 also rotates. The larger gear 101b rotates a threaded portion of a ball screw (hereinafter also called the screw) 102, and this rotational motion is converted into a linear motion by a ball screw nut 103 (hereinafter simply called the nut). As the servomotor 100 rotates, both a table 104 connected to the nut 103 and a work 105 supported on the table 104 are moved axially of the ball screw 102 (hereinafter simply called "axially" or "longitudinally" by this conversion. The balls crew 102 is supported at opposite ends by a pair of brackets 107a, 107b via a motor-side bearing 106a and a counter-motor-side bearing 106b, the brackets 107a, 107b being rigidly connected to a machine frame. A motor position detector 108 is connected to the servomotor 100 to detect the motor position in rotation and, at the same time, to detect the position of an object (hereinafter also called the table position) indirectly.
In FIG. 1, L represents an entire length of the ball screw 102 and x represents a distance between the motor-side end of the screw 102 and the table position. Each of distances between the motor-side end of the screw 102, the gear shafts and the motor-side bearing 106a is negligibly small as compared to distance x on the motor-side leg of the stroke of the table 104. The distance between the gear shaft and the table position and the distance between the motor-side bearing 106a and the table position are designated by x. In a ball screw drive system which drives the table via this ball screw, the position, speed, and propulsive force of the table are indirectly controlled by controlling the rotational position, speed, and torque of the servomotor.
FIG. 2 is a block diagram of a conventional semi-closed position control apparatus employing a ball screw system as an object system. To this conventional position control apparatus, a position command value X from a non-illustrated host apparatus is given. In the semi-closed position control, the motor position xm is defined as a position feedback xf. A subtracter 50 calculates a position deviation (X-xf), and an amplifier 51 multiplies this calculated position deviation by a position loop gain Kv. A speed command value V, which is obtained by differentiating the position command value X by a differentiator 57, is added to the output of the amplifier 51 by an adder 52, whose output is to be used as a speed command input Vma. Another subtracter 54 subtracts a motor speed obtained by differentiating the motor position xm by a differentiator 53, from Vma to thereby calculate a speed deviation (V-vm). This speed deviation (V-vm) is amplified in proportional integration by a speed amplifier section 55. Simultaneously, a differentiator 58 differentiates the speed command value V to thereby calculate an acceleration command value A. Further, a value obtained by multiplying the acceleration command value A by a torque command conversion factor K1 is added to the amplified speed deviation as a torque command value .tau.ca by an adder 56.
A power amplifier section 60 composed of a non-illustrated power amplifier and a non-illustrated servomotor amplifies the torque command value .tau.ca into a motor output torque .tau.; its amplification factor is represented by a torque conversion constant Ct. An object system 61 is the ball screw drive system of FIG. 1, and the motor feed position xm indirectly the table position. These differentiators 57, 58, 59 constitute a feedforward system to realize an improved response of position control. S of the individual differentiator 57, 58, 59 stands for a Laplace operator defining a differential function.
The manner in which the torque is transmitted in the ball screw drive system will now be described using FIG. 3 and contrasted to FIGS. 1 and 2. FIG. 3 schematically shows a model of the ball screw drive system as converted with respect to the motor axis. The motor output torque .tau. is transmitted to the table via the motor gear train and the screw. Km and Kc are a torsional rigidity of the motor shaft and a torsional rigidity of the gear shaft, respectively, while Kb(x) is a torsional rigidity of the screw at a distance x from the motor-side end of the gear shaft to the table position. Km, Kc and Kb(x) collectively stand for an integrated torsional rigidity Kt existing between the motor and the table. A table transmission torque .tau.r is a torque to be transmitted to the table, and the screw is subject to this torque reaction longitudinally, i.e., axially.
Kn is a thrust rigidity of the nut, and Kbl(x) and Kbr(x) are a motor-side thrust rigidity and a counter-motor-side thrust rigidity, respectively, at the distance x from the motor-side bearing on the screw to the table position. Likewise, Kgl and Kgr represent a motor-side thrust rigidity and a counter-motor-side-bearing thrust rigidity, respectively. Likewise, Krl and Krr each represent a thrust rigidity as substituted for the flexural rigidity when a beam is supported as a cantilever by the motor-side bracket or the counter-motor-side bracket. Ksl is a thrust rigidity on the motor side which is an integrated value of Krl, Kgl and Kbl(x); and Kisr is a thrust rigidity on the counter-motor-side which is an integrated value of Krr, Kgr and Kbr(x); and Ks is an integrated thrust rigidity existing between the table and the machine frame which rigidity is obtained by collecting Krl, Kgl, Kbl(x), Ksr, Krr, Kgr, Kbr(x) all together.
.tau.d represents a turbulence torque (such as cutting torque or gravitational torque) acting outwardly from the table. Xm represents a feed position by the motor, xL represents a table movement position in the direction of rotation of the ball screw, and xo represents a starting position of the table in the direction axial of the ball screw; as a result, a real position (not shown) xi of the table is represented by xi=xL+xo. IL represents a load-side inertial moment (composite inertial moment of table plus work), and Is represents a motor-side inertial moment (composite inertial moment of motor plus gear plus screw). Torque, rigidity, position and inertial moment are all regarded as having the same converted value on the motor shaft.
The manner in which the ball screw drive system of FIG. 3 is operated at an adjustable speed in the conventional semi-closed position control apparatus will now be described. During the adjustable driving, a table transmission torque .tau.r can be expressed by the following equation (1): EQU .tau.r=IL.multidot.L+.tau.d (1)
wherein aL is a twice-differential of the movement position xL indicating an acceleration of the table movement. At the same time, a deflection expressed by the following equation (2): EQU xm-xL=.tau.r/Kt EQU xo=-.tau.r/Ks (2)
occurs in the ball screw drive system. Namely, between the feed position xm by the motor and the real position xi of the table, a position deviation expressed by the following equation (3), which is obtained from equation (2), occurs. ##EQU1##
Thus, during the adjustable driving, the feed position xm by the motor and the real position xi of the table do not coincide. As a consequence, in the conventional semi-closed position control apparatus with a position feedback xf defined by the feed position xm, controlling the real position of the table in accordance with the position command value X much precisely, which is the objective of this conventional concept.
FIG. 4 is a block diagram of a conventional full-closed position control apparatus in which a non-illustrated direct position detector, such as a linear encoder, mounted on the ball screw drive system directly detects a real position xi of the table as a position feedback xf. In FIG. 4, parts or elements similar to those of FIG. 2 are designated by the same numbers and labeled with the same names, and their description is not repeated here. In this conventional apparatus, since the real position of the table is feedbacked, it is possible to regularly control the real position of the table in accordance with the position command value X, even if a position deviation due to the deflection of the ball screw drive system has occurred during adjustable driving. However, a responsibility is determined by a position loop gain Kv. The larger the loop gain Kv, the higher the responsibility; however, the set value of Kv is limited due to the integrated rigidity of the ball screw drive system and hence cannot be set so high usually. Therefore, when the table is driven at a non-constant speed, i.e., at an adjustable speed, it is particularly difficult to precisely control the real position of the table in accordance with the position command value X as the position deviation resulting from the deflection is influential on such control.
FIG. 5 is a block diagram showing another conventional full-closed position control apparatus. In FIG. 5, as for FIG. 4, parts or elements similar to those of FIG. 2 are designated by the same numbers and labeled with the same names, and their description is not repeated here. In this conventional full-closed position control apparatus, the feed position xm by the motor is subtracted from the real position xi of the table by a subtracter 62. A function unit 63 is added to the output of the subtracter 62, and the output is added to the feed position xm (by the motor) in an adder 64 to create a position feedback xf. For the function unit 63, a function G(s), such as a movement average process or a first-order lag process, is selected such that its output increases with lapse of time with respect to the step input to become normally: input=output.
Accordingly, by defining the position feedback so as to satisfy xf.apprxeq.xm with respect to a high-frequency position command value X and so as to satisfy xf.apprxeq.xi with respect to a low-frequency position command value X, this conventional apparatus directly controls the table position regularly with keeping the safety of the full-closed position control, which could not easily been realized until the development of this conventional technology. Even when such composite position feedback, it is impossible to control a possible position deviation, which might occur due to the deflection of the ball screw drive system during adjustable driving, likewise in the conventional apparatus of FIG. 2, as long as the position feedback satisfies xf.apprxeq.xm. At that time, even if the position feedback satisfies xf.apprxeq.xi, it is also difficult to control the position deviation, which is also true for likewise the conventional apparatus of FIG. 4. Even in the full-closed position control apparatus using a composite position feedback, because of influence of the position deviation due to the deflection, it is particularly difficult to precisely control the table position precisely in accordance with the position command value X.
As is understood from the foregoing description, when a ball screw drive system driving the table position through a ball screw is positionally controlled, a dynamic deflection resulting from an integrated rigidity existing between the table and the machine frame and an integrated torsional rigidity existing between the motor and the table would occur. In the conventional semi-closed position control apparatus, full-closed position control apparatus or full-closed position control apparatus using a composite position feedback, because of this dynamic deflection, it is difficult to control the table position at high precision in accordance with the position command value.